Question

What is the 11th term of an AP whose 5th term is 19 and 15th term is 59? pls give nly the answrs

Answer 1

EXPLANATION.

• GIVEN

5th term of an Ap = 19,

15th term of an Ap = 59

Find it's 11th term

according to the question,

T5 = a + 4d = 19 ...... (1)

T15 = a + 14d = 59 ..... (2)

From equation (1) and (2) we get,

- 10d = - 40

d = 4

put the value of d = 4 in equation (1)

a + 4(4) = 19

a + 16 = 19

a = 3

Tn = a + ( n - 1 ) d

T11 = a + 10d

3 + 10(4)

3 + 40

43

Therefore,

11th term of an Ap = 43

Answer 2

Question :-

What is the 11th term of an AP whose 5th term is 19 and 15th term is 59.

Given :-

• 11 th term = ?
• 5th term = 19
• 15th term = 59

Solution :-

Using ᵃn Formula in both given term

• 5th term = a +( 5 - 1 ) d = 19

→ a + 4 d = 19 ----equ(1)

• 15th term = a + ( 15 - 1 ) d = 59

→ a + 14 d 59 ----equ(2)

Now,

Solving both equation simultaneously

→ a + 4 d = 19

→ $\sf{\underline{ a_- +_-<em> </em>14 d =_-59}}$

→ $\sf - 10 d = -40$

→ d = 40/10

→ d = 4

• Putting the value of d in both equation

→ a + 4d = 19

→ a + 4 × 4 = 19

→ a = 19 - 4 × 4

→ a = 3

• Similarly in equation (2)

→ a + 14d = 59

→ a + 14 × 4 = 59

→ a = 59 - 14 × 4

→ a = 3

Now,

• Finding 11th term

$\sf → a_n = a + ( n - 1 ) d$

$\sf → a _{11} = 3 + ( 11 - 1 ) 4$

$\sf → a_{11} = 3 + 10 × 4$

$\sf → a _ {11} = 3 + 40$

$\sf → a_{11} = 43$

Hence :-

• the 11the term is = 43